Spectral decomposition of normal operator in real Hilbert space

Spectral Theory of Operator Measures in Hilbert Space

In §2 the spaces L2(Σ,H) are described; this is a solution of a problem posed by M. G. Krĕın. In §3 unitary dilations are used to illustrate the techniques of operator measures. In particular, a simple proof of the Năımark dilation theorem is presented, together with an explicit construction of a resolution of the identity. In §4, the multiplicity function NΣ is introduced for an arbitrary (non...

Operator Preconditioning in Hilbert Space

2010 1 Introduction The numerical solution of linear elliptic partial differential equations consists of two main steps: discretization and iteration, where generally some conjugate gradient method is used for solving the finite element discretization of the problem. However, when for elliptic problems the dis-cretization parameter tends to zero, the required number of iterations for a prescrib...

Operator Extensions on Hilbert Space

Hilbert Space of Real Sequences

One can prove the following two propositions: (1) The carrier of l2-Space = the set of l2-real sequences and for every set x holds x is an element of the carrier of l2-Space iff x is a sequence of real numbers and idseq(x) idseq(x) is summable and for every set x holds x is a vector of l2-Space iff x is a sequence of real numbers and idseq(x) idseq(x) is summable and 0l2-Space = Zeroseq and for...

OPERATOR THEORY ON HILBERT SPACE Class notes